This paper studies the new families of exact traveling wave solutions with the modified nonlinear Schrödinger equation, which models the propagation of rogue waves in ocean engineering. The extended Fan sub-equation method with five parameters is used to find exact traveling wave solutions. It has been observed that the equation exhibits a collection of traveling wave solutions for limiting values of parameters. This method is beneficial for solving nonlinear partial differential equations, because it is not only useful for finding the new exact traveling wave solutions, but also gives us the solutions obtained previously by the usage of other techniques (Riccati equation, or first-kind elliptic equation, or the generalized Riccati equation as mapping equation, or auxiliary ordinary differential equation method) in a combined approach. Moreover, by means of the concept of linear stability, we prove that the governing model is stable. 3D figures are plotted for showing the physic...

中文翻译：

---

修正的非线性Schrödinger方程的调制不稳定性分析，光学和其他解决方案

本文利用修正的非线性Schrödinger方程研究了精确行波解的新族，该方程对海洋工程中流浪的传播进行了建模。具有五个参数的扩展Fan子方程法用于找到精确的行波解。已经观察到，该方程式表现出行波解的集合，用于限制参数值。该方法对于求解非线性偏微分方程是有益的，因为它不仅对找到新的精确行波解有用，而且还为我们提供了以前通过使用其他技术（Riccati方程或一类椭圆方程）获得的解。 ，或将一般Riccati方程作为映射方程，或将辅助常微分方程方法）组合起来使用。此外，通过线性稳定性的概念，证明了控制模型是稳定的。绘制3D图形以显示物理...